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SIMPLIFYING ALGEBRAIC EXPRESSIONS •ADDING LIKE TERMS •MULTIPLYING LIKE TERMS •SIMPLIFYING EXPRESSIONS •REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION •USING FORMULAS •REMOVING BRACKETS ADDING LIKE TERMS 3+3+3+3 4 X3 This gives the a+ a+a +a 4a Can be written in the shorter form Meaning that we have 4 bundles of 3’s VALUE 12 Can be written in the shorter form We cannot give a value for 4a until we are given a value for a If a=7 4a = Then by replacing a with 7 4 x(7) = 28 So a value for the expression 4a when a = 7 is 28 Some examples Simplify the following expressions 3a + 2a = a+a+a + Combine all the a’s together to get one term a+a = 5a 5b – 2b = b+b+b+b+b = 3b - b+b Take 2 b’s away from the 5 b’s Simplifying expressions with numbers and different letters Simplify 3a + 2b + 5a + 3b + 7 3a + 5a + 8a + 2b + 3b 5b 8a + 5b +7 + + 7 7 WE can only add or subtract like terms to each other Multiplying like terms Can be written in the shorter form 2 X 2 X 2 X 2 X2 This means that 2 is multiplied by itself 5 times 25 This gives a value aXaXaXaXa a5 32 Can be written in the shorter form We cannot get a value for a5 until we are given a value for a If a = 7 then a5 = 75 =16807 So a value for the expression when a = 7 is 16807 a5 Some examples Simplify the following expressions 3a x a =3xaxaxa x a = 3b x 2b We now have 3 times a multiplied by itself 4 times 3 a4 =3x2 =6 =6 x x b2 bxb b2 Multiply the numbers together and multiply the letters together Write product without multiplication sign Examples with numbers and letters 3b2 X 4b3 3X4 12 12 b2X b3 X X X bXb X bXbXb b5 Multiply the numbers together b2X b3 = b2+3 Add the powers =b5 Simplify REMEMBER r = r1 4r x 6s x r2 x s3 = 4x6 x x s x s3 Multiply similar letters together by adding the powers Multiply the numbers together 24 r x r2 x r1+2 =24 r3s4 x s1+3 When we multiply letters and numbers first put the numbers next the letters in alphabetical order and we do not need the X sign Order of operations 5+2x3 = 11 Not 21 In mathematics we have rules Multiplication or division is calculated before addition or subtraction 2xa +5 6–2xb Is simplified to Is simplified to 2a + 5 6-2b Have you got it yet ? Simplify the following 1. 2a + 3a 2. 3a + 4b + 2a + 5b 5a 5a + 9b 8 . 3m + 2m + 7 9. 6j – 3j + j 5m+ 7 4j b4 10. 3s x 4s x 6 72b2 4. b x b x c x c x c b2c3 11. 3 x s + 7 3s+7 5. 4b2 x 5b3 20b5 12. 6 + 3 x d 6+3d 6. 3c x 4b 12bc 13 . 10n – 2 x 3n 4n 7. 2 c 4 + 3c4 5c4 14. 8b – 3 x b2 3. b x b x b x b 8b –. 3 b2 Finding values for expressions Find a value for the expression 3b = 3b when b =7 3 x (7) = 21 Take out b and replace it with 7 Put 7 inside a bracket 21 is the value of the expression Find a value for the expression 3c + b when c = 2 and b = 5 3c + b = 3 x (2) + ( 5) Replace c with 2 and b with 5 = 6+5 = 11 11 is the value of the expression Find a value for the expressions a) pq b) 2p + q c) 5pq +2p e) 3 ( p + 2q ) f) ( p + q ) 2 when p = 3 and q = 7 a) pq b) 2p + q = (3) x (7) = 2 x ( 3) + ( 7 ) = 21 = 6 = 13 d) q2 - p2 = (7)2 - (3)2 = 49 - 9 = 40 + 7 e) 3 ( p + 2q ) = 3 ( (7) + 2x(3) ) = 3( 7 + 6) = 3 x 13 = 39 d) q2 - p2 when c) 3pq + 2p = 3x(3)x(7)+2x(3) = 63 + 6 = 69 f) (q-p)2 = ( (7) – (3) ) 2 =(4)2 = 16